Asymptotic behaviour of the cross-variation of some integral long memory processes
Résumé
We study the asymptotic behaviour of the cross-variation of two-dimensional processes having the form of a Young integral with respect to a fractional Brownian motion of index $H>\frac12$. When $H$ is smaller than or equal to 3/4, we show asymptotic mixed normality. When $H$ is stricly bigger than 3/4, we obtain a limit that is expressed in terms of the difference of two independent Rosenblatt processes.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)